The modern conception of gravity began in the seventeenth
century with Sir Isaac Newton. At the basis of Newton's Universal
Law of Gravitation is a simple empirical observation:Everything happens... as if the force between two bodies is
directly proportional to the product of their masses and inversely
proportional to the square of the distance between them.
- Sir Isaac Newton
This plain fact explained the detailed motion of the moon,
encapsulated Kepler's Laws of planetary motion, and in the
modern day informs us how to navigate tiny spacecraft through
the vast expanses of interplanetary space with remarkable
precision. Never in history has any such plainspoken observation
carried us (literally!) so far.

Newton's law of gravity has been tested over a wide range of
scales, from the submillimeter to the solar system. Its repeated
successes and incredible accuracy is rivaled by few other physical
theories. The trustworthiness of Universal Gravitation was such
that in the nineteenth century
the tiny excess precession of Mercury's orbit constituted a crisis.

This crisis was resolved by Einstein's theory of General
Relativity, the only significant update to our conception of
gravitation since Newton. General Relativity has itself withstood
many precision tests.
The repeated successes of Newton-Einstein theory, and the sheer
eminence of its authors, has led to a widespread attitude among
scholars that there can be nothing new to learn about gravitation.
Many of these same authors simultaneously adhere to the contradictory
attitude that there
must be a unified theory of everything, or at least of the four
fundamental forces. So far, gravity has steadfastly refused to be
assimilated into the quantum mechanical picture which is essential
to the description of the other forces of nature. Yet there must be
a quantum theory of gravity. Pursuing this to its
logical conclusion, there must be yet more to learn beyond what
Newton and Einstein have already told us.

Beyond the quantum realm, there are other gravitational puzzles
that remain to be explained. One of the most pertinent is
commonly referred to as "the dark matter problem." When
astronomers measure the motions of stars and gas in galaxies and
yet larger systems, they find that speeds are well in excess of what
can be explained by the application of Netwon's Universal
Gravitation to the mass in visible forms such as stars
(see Figure 1).
This has led to the inference that most (roughly 90%) of the mass in
the universe is dark.

There is a tremendous amount of evidence for dark matter. Yet
all of this evidence is based on the assumption that Newtonian
theory can safely be extrapolated from the solar system
(where it is well tested) to the scales of galaxies.
While an excellent starting point, we should
not presume that it will indeed hold. Sticklers for epistemology
might object that, strictly speaking, we are faced not with
evidence for dark matter, but rather for mass discrepancies. What
we see doesn't add up, so either the universe is full of unseen mass,
or the theory which leads to the inference of this mass needs
revision.

To return to gravity's empirical roots, recall Newton's observation
that "everything behaves as if..." While this is true with great
accuracy in the solar system, it is patently false in galaxies and
other extragalactic systems. If it held, we would have no need for
dark matter. Casting the blame instead on gravity might be
appropriate if there exists a modification of Newton's formula
which satisfies the spirit of his dictum
"everything behaves as if..."

Many such attempts have been made, and many have failed.
These failures encouraged people in the direction of dark matter.
Yet there is one idea which has yes to fail.
In 1983, Israeli physicist M. Milgrom
hypothesised a specific change in the equations
governing particle motions at very low accelerations. He
called this the modified Newtonian dynamics, or MOND. MOND reduces
to the usual Newtonian form in the regime of high acceleration,
but at accelerations lower than 1 part in 1011 of what we feel here
on earth, things change in a way that might account for the mass
discrepancy.

Once the equations of MOND (or any other hypothesised
modification) are written down, they leave little room for
maneuver. Accurate dynamical data, such as the rotation curves of
spiral galaxies, must follow from the application of MOND to the
observed distribution of luminous matter (stars and gas). Each and
every galaxy provides a unique test of the hypothesis. Fits to the
observed rotation curves of galaxies like that in
Fig. 1 have now
been performed for over 100 galaxies, with comparable results.
While there is certainly the occasional puzzle, there are no known
cases where MOND clearly fails. In the vast majority, it clearly
succeeds. MOND is the formula which satisfies Newton's dictum
"everything behaves as if..."

In his original 1983 papers, Milgrom made a series of predictions
about a then unknown class of 'low surface density' galaxies. These
objects should, if MOND is correct, exhibit large mass discrepancies
because their diffuse luminous mass would provide an even
weaker gravitational acceleration than the already tenuous
amount found in brighter galaxies. He listed a number of specific,
testable consequences of this prediction. At the time, such objects
were thought to be rare or nonexistent. Later they were
discovered, and are now known as 'low surface brightness'
galaxies. In the process of studying these new objects for their
own interest, astronomers gradually accumulated the data
necessary to test Milgrom's largely forgotten, decade old
predictions. It came as quite a shock to find that every one of them
was realised in the data. While science in principle advances by the
construction of hypotheses that make predictions which can
subsequently be tested, it is a rare case indeed that in practice
actually follows this model so cleanly.

These successes of MOND are most obvious in places where the
dynamical data which test it are most accurate. However, there
are many other systems where the picture is less clear. Any
modification of dynamical laws must explain the mass discrepancy
everywhere. It must work not only for rotation curves, but also for the
velocity dispersions of spheroidal galaxies, the gas temperatures of
clusters of galaxies, and the peculiar motions of galaxies
in the large scale structure of the universe.

One place MOND appears to have serious difficulties is in rich
clusters of galaxies: the
luminous mass falls short by a factor of roughly two of what is
needed to explain the observations. On the one hand, this may not
seem so bad: coming within a factor of two in astronomy is often
viewed as a great success. On the other hand, the
discrepancy does appear genuine. This implies that there remains
some additional mass yet to be discovered in clusters. This, in
effect, invokes some form of dark matter - hardly a selling point for a
theory which seeks to do away with such stuff. This might be
considered fatal for MOND were it not for the fact that the
discovery of huge reservoirs of mass in clusters has happened
before. It was long thought that the stars in the galaxies which made up the
clusters were the biggest reservoir of normal matter there.
About a decade ago, it became apparent that the mass of hot, diffuse gas
spread between the cluster galaxies greatly exceeds the mass in
stars. This being the case, it
is hard to be confident that another factor of two won't turn up.

Another problem is cosmology. Unmodified General Relativity provides
a satisfactory interpretation for the empirical aspects of the hot big
bang cosmology - an expanding universe, nucleosynthesis of the light
elements, and the relic radiation known as the cosmic microwave background.
The success of standard cosmology is often equated with evidence against
MOND. Yet the standard cosmology is only viable if
90% of the mass indeed exists in an as yet hypothetical form -
hardly a great boasting point. Worse, in recent years it has become
necessary to revive Einstein's self-described "greatest blunder":
the cosmological constant. One might wonder if these strange turns
are hinting at some greater truth.

The cosmic microwave background may help to decide this issue.
A universe full of dark matter leaves a subtly different
signature on this echo of the big bang than does one devoid of dark
matter. Recent observations came tantalizingly close to being able
to distinguish between the two cases, but ultimately failed to make
a clear distinction. Upcoming space missions, like NASA's MAP and
ESA's PLANCK, will hopefully do the trick.

Regardless of whether MOND is correct as a theory, it does
constitute an observed phenomenology which demands
explanation. Herein lies a real conundrum for the dark matter
picture. The natural expectations of dark matter theories for
rotation curves do not look like MOND, and hence fail to reproduce
a whole set of essential observational facts. The best a dark matter
theory can hope to do is contrive to look like MOND, and hence
postdict the many things which Milgrom successfully predicted.
This gives one genuine pause to consider how science is suppose to
proceed.

The debate between dark matter and MOND is refreshing. There
has been some concern expressed in recent years that science is at
its end. All the fundamental discoveries have been made; there is
nothing truly new left to discover. This sentiment echoes the
words of Rutherford nearly a century ago: "All that remains... is to fill
in the last few decimal points." Now, as then, the rumors of the end
of fundamental science are greatly exaggerated.

Figure 1: The rotation curve of the dwarf galaxy NGC 1560.
The lower line is the rotation predicted by the
application of Newtonian gravity to the observed stars and gas.
This falls well short of the observed rotation, leading to the
inference of dark matter to make up the difference. The upper
line shows the rotation is expected by the application of MOND to
the observed stars and gas. Similar results are now known for over
100 galaxies. Note that in this case, even the kink observed in the
gas distribution is reflected in the rotation. This is exceedingly
difficult to explain with dark matter which is not distributed like
the luminous mass. MOND is the formula which satisfies the
Newton's dictum "everything behaves as if..."